Section 9.3: Probability Rules

This section explains key probability rules: addition rule, multiplication rule, complement rule, and conditional probability.

Example 1: Addition Rule

A deck has 52 cards. What is the probability of drawing a red card or a King?

Step 1: Count red cards: 26, Kings: 4, Red Kings overlap: 2

Step 2: Use addition rule: P(Red ∪ King) = P(Red) + P(King) - P(Red ∩ King)

P = 26/52 + 4/52 - 2/52 = 28/52 = 7/13

Example 2: Multiplication Rule

Rolling two dice, probability both show a 6?

Step 1: Probability first die is 6: 1/6

Step 2: Probability second die is 6: 1/6

Step 3: Use multiplication rule: 1/6 * 1/6 = 1/36

Practice Problems

  1. From a standard deck, probability of drawing a face card or a heart?
  2. Flip 3 coins. Probability of all heads?
  3. Probability of rolling an even number or a multiple of 3 on a die?
  4. Probability of not drawing a spade from a deck?
  5. Two dice rolled. Probability sum is 7 and first die shows 3?
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